QHWM of the orthogonal and symplectic types Lie subalgebras of the Lie\n algebra of the matrix quantum pseudo differential operators

2017/03/17 by Karina Batistelli, Batistelli, Karina, Carina Boyallían +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1703.06175

Abstract

In this paper we classify the irreducible quasifinite highest weight modules\nover the orthogonal and symplectic types Lie subalgebras of the Lie algebra of\nthe matrix quantum pseudo differential operators. We also realize them in terms\nof the irreducible quasifinite highest weight modules of the Lie algebras of\ninfinite matrices with finitely many nonzero diagonals and its classical Lie\nsubalgebras of types B, C and D.\n

Related

• Lie subalgebras of the matrix quantum pseudo differential operators
• Quasifinite representations of W_∞
• Representations of D_q(k [x])
• Quasifinite representations of classical Lie subalgebras of W_1+infty
• Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them